Can someone please weigh in and let me know if this is something I even have a shot at?

I'm a prospective PhD student in statistics hoping to get a better idea of my chances. I'm interested in Bayesian stats and its applications in machine learning.

I have no idea where I stand so any help would be greatly appreciated. Some preliminary data:

Undergrad Institution: US News 35-40

Major(s): BA Mathematics

Minor(s): Spanish

GPA: 3.9

Type of Student: Domestic White Male

GRE General Test:

Q: 164 (88%)

V: 162 (89%

W: 4.5 (72%)

GRE Subject Test in Mathematics:

Have not taken yet. Should I?

Programs Applying: UCLA (PhD stats), UCI (PhD Stats), USC (PhD Stats), Caltech (PhD applied and Comp. Math).

I'll be looking to apply this fall, and hoping to move to LA for personal reasons. Do I have a shot at these schools. Any suggestions of other programs I'd be competitive for if I don't end up in LA?

Research Experience: Just a Python-centric data science independent research course this semester. No publication.

Awards/Honors/Recognitions: Typical Dean's list etc.

Pertinent Activities or Jobs: Internships with BlueCross, Marriott, tech analyst. Served 2 year mission in Chile.

Letters of Recommendation: (3, personal, but none are particularly well known: algebraist, probabilist, machine learning)

My main concern is that I switched from a stats BS to a math BA and as such my coursework for a math major is pretty weak.

Coursework:

Calc 1-3 (A,A,A)

Linear Algebra and Diff Eqs (A)

Linear Algebra- Proof based (A-)

Honors Real Analysis (A-)

Probability (A)

Bayesian Stats (A)

Stats 1-2 (A,A)

THOUGHTS? Thank you so much!